Nothing compares 2 this feud! Miley Cyrus and Sinead O'Connor's war of words -- with many, many more words coming from O'Connor's side -- continues. After the Irish-born '90s singer, 46, furiously chided the pop star, 20, in a second, lengthy "open letter" on her website, Cyrus retorted for the second time via Twitter late Thursday, Oct. 3 -- and, just as quickly, O'Connor threatened to sue.

"Sinead. I don't have time to write you an open letter cause Im hosting & performing on SNL this week," the "Wrecking Ball" provocateur (who indeed will be on the Saturday, Oct. 5 installment of Saturday Night Live) sniped. "So if you'd like to meet up and talk lemme know in your next letter. :)"

UPDATE: O'Connor then replied with a third letter via Facebook -- this time suggesting potential legal action. Addressed to "Miley," the missive begins: "I have no interest whatsoever in meeting you. You had plenty of time yesterday to abuse Amanda Bynes .. an entirely innocent party.. and myself.. who also did nothing to deserve your abuse.. along with every other sufferer of mental health problems and every person who suffered abuse at the hands of priests."

The feud began when O'Connor, whom Cyrus called a "role model," published an initial "open letter" chastising Cyrus for her hyper-sexual persona and warning her not to "prostitute" herself. The former Disney starlet replied by comparing O'Connor to troubled actress Amanda Bynes -- currently seeking psychiatric treatment -- and sharing a snapshot of O'Connor's infamous "SNL" appearance in which she shredded a photo of the Pope on the air.

O'Connor continues in her third letter: "You can take five minutes today between g- string [expletive] changes to publicly apologise and remove your abusive tweets. If you do not then you don't give a [expletive] who you mock and what damage you do by being so ignorant.When you publicly apologise to Amanda and myself and all mental health sufferers as well as all who were abused by priests that will end the matter as far as I am concerned.

"What you did yesterday was designed to damage me and my career and has caused me enormous distress and harassment and has potential to damage my career, since you deliberately gave the impression those tweets of mine were not two years old but reflect my current condition," the letter continues. "If you cannot apologize I will have no choice but to bring legal proceedings against you since it is extremely hard to be given work when people think one is suffering from mental illness. I have no interest in or desire to cause you trouble but if you do not apologise for having deliberately tried to cause me hurt and trouble personally and professionally I will have to bring pressure upon you. When you end up in the psych ward or rehab I'll be happy to visit you.. and would not lower myself to mock you."

The rant went on: "Cease behaving in an anti-female capacity. You will become the victim of it shortly. Soon it will be you the media 'crazy' .. and you will not enjoy it.. and you will appreciate people (like myself) standing up for you. Which I will be happy to do.. if you earn my respect today by apologising publicly."

As it happens, Cyrus unveiled brand-new photos sure to shock her fans and detractors in a whole new way: NSFW photos by her "Wrecking Ball" director Terry Richardson, in which she barely conceals her genitals in an extremely skimpy leotard, and bares her breasts through a sheer fishnet top.